Cover Image

Understanding Generalization in Physics Informed Models through Affine Variety Dimensions

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Koshizuka, Takeshi, Sato, Issei
Format:	Preprint
Published:	2025
Subjects:	Machine Learning Statistics Theory
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Understanding the Expressivity and Trainability of Fourier Neural Operator: A Mean-Field Perspective
by: Koshizuka, Takeshi, et al.
Published: (2023)

Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions
by: Kanj, Haitham, et al.
Published: (2026)

Understanding Overparametrization in Survival Models through Interpolation
by: Liu, Yin, et al.
Published: (2025)

Sparse Max-Affine Regression
by: Kanj, Haitham, et al.
Published: (2024)

Benign overfitting in Fixed Dimension via Physics-Informed Learning with Smooth Inductive Bias
by: Wong, Honam, et al.
Published: (2024)

Information Geometry of Wasserstein Statistics on Shapes and Affine Deformations
by: Amari, Shun-ichi, et al.
Published: (2023)

Affine Invariance in Continuous-Domain Convolutional Neural Networks
by: Mohaddes, Ali, et al.
Published: (2023)

Dimension-free Score Matching and Time Bootstrapping for Diffusion Models
by: Kumar, Syamantak, et al.
Published: (2025)

Convergence of Diffusion Models Under the Manifold Hypothesis in High-Dimensions
by: Azangulov, Iskander, et al.
Published: (2024)

Generalized Robust Adaptive-Bandwidth Multi-View Manifold Learning in High Dimensions with Noise
by: Ding, Xiucai, et al.
Published: (2026)

On the Statistical Properties of Generative Adversarial Models for Low Intrinsic Data Dimension
by: Chakraborty, Saptarshi, et al.
Published: (2024)

Jointly Modeling and Clustering Tensors in High Dimensions
by: Cai, Biao, et al.
Published: (2021)

Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixing
by: Xu, Danru, et al.
Published: (2026)

Kernel Two-Sample Tests in High Dimension: Interplay Between Moment Discrepancy and Dimension-and-Sample Orders
by: Yan, Jian, et al.
Published: (2021)

Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space
by: Kan, Kelvin, et al.
Published: (2026)

PAC-Chernoff Bounds: Understanding Generalization in the Interpolation Regime
by: Masegosa, Andrés R., et al.
Published: (2023)

Dimension-Free Bounds for Generalized First-Order Methods via Gaussian Coupling
by: Reeves, Galen
Published: (2025)

Dimension lower bounds for linear approaches to function approximation
by: Hsu, Daniel
Published: (2025)

Learning Curves and Benign Overfitting of Spectral Algorithms in Large Dimensions
by: Lu, Weihao, et al.
Published: (2026)

Double Descent: Understanding Linear Model Estimation of Nonidentifiable Parameters and a Model for Overfitting
by: Christensen, Ronald
Published: (2024)

Belted and Ensembled Neural Network for Linear and Nonlinear Sufficient Dimension Reduction
by: Tang, Yin, et al.
Published: (2024)

A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity
by: Jia, Zeyu, et al.
Published: (2025)

The Catastrophic Failure of The k-Means Algorithm in High Dimensions, and How Hartigan's Algorithm Avoids It
by: Lederman, Roy R., et al.
Published: (2026)

The $φ$ Curve: The Shape of Generalization through the Lens of Norm-based Capacity Control
by: Wang, Yichen, et al.
Published: (2025)

Dimension-Free Convergence of Diffusion Models for Approximate Gaussian Mixtures
by: Li, Gen, et al.
Published: (2025)

TrIM: Transformed Iterative Mondrian Forests for Gradient-based Dimension Reduction and High-Dimensional Regression
by: Baptista, Ricardo, et al.
Published: (2024)

Dimension-agnostic inference using cross U-statistics
by: Kim, Ilmun, et al.
Published: (2020)

A Limit Theory of Foundation Models: A Mathematical Approach to Understanding Emergent Intelligence and Scaling Laws
by: Shu, Jun, et al.
Published: (2026)

Dimension-free error estimate for diffusion model and optimal scheduling
by: de Bortoli, Valentin, et al.
Published: (2025)

Solving PDEs on Spheres with Physics-Informed Convolutional Neural Networks
by: Lei, Guanhang, et al.
Published: (2023)

Hypothesis Testing for Generalized Thurstone Models
by: Makur, Anuran, et al.
Published: (2025)

Understanding Learning Invariance in Deep Linear Networks
by: Duan, Hao, et al.
Published: (2025)

Understanding Aggregations of Proper Learners in Multiclass Classification
by: Asilis, Julian, et al.
Published: (2024)

Generating Rectifiable Measures through Neural Networks
by: Riegler, Erwin, et al.
Published: (2024)

Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs
by: Zhao, Yuxuan, et al.
Published: (2026)

Confidence Sequences for Generalized Linear Models via Regret Analysis
by: Clerico, Eugenio, et al.
Published: (2025)

Provable Efficiency of Guidance in Diffusion Models for General Data Distribution
by: Li, Gen, et al.
Published: (2025)

Inference for Deep Neural Network Estimators in Generalized Nonparametric Models
by: Meng, Xuran, et al.
Published: (2025)

Dimension-free bounds in high-dimensional linear regression via error-in-operator approach
by: Noskov, Fedor, et al.
Published: (2025)

Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution
by: Vardanyan, Elen, et al.
Published: (2023)